The quantitative relation between transcription factor concentrations and the rate of protein production from downstream genes is central to the function of genetic networks. Here we show that this relation, which we call the gene regulation function (GRF), fluctuates dynamically in individual living cells, thereby limiting the accuracy with which transcriptional genetic circuits can transfer signals. Using fluorescent reporter genes and fusion proteins, we characterized the bacteriophage lambda promoter P_R in Escherichia coli. A novel technique based on binomial errors in protein partitioning enabled calibration of in vivo biochemical parameters in molecular units. We found that protein production rates fluctuate over a time scale of about one cell cycle, while intrinsic noise decays rapidly. Thus, biochemical parameters, noise, and slowly varying cellular states together determine the effective single-cell GRF. These results can form a basis for quantitative modeling of natural gene circuits and for design of synthetic ones.